Corollary 8.5.1.17. Let $X$ and $Y$ be Kan complexes and let $\kappa $ be an uncountable cardinal. Suppose that $Y$ is a retract of $X$ in the $\infty $-category $\operatorname{\mathcal{S}}$. If $X$ is essentially $\kappa $-small, then $Y$ is essentially $\kappa $-small.

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